Compactness of Green operators with applications to semilinear nonlocal elliptic equations

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F25%3A00144250" target="_blank" >RIV/00216224:14310/25:00144250 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0022039624007356" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0022039624007356</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jde.2024.11.019" target="_blank" >10.1016/j.jde.2024.11.019</a>

Result language
angličtina
Original language name
Compactness of Green operators with applications to semilinear nonlocal elliptic equations
Original language description
In this paper, we consider a class of integro-differential operators L posed on a C2 bounded domain Ω⊂RN with appropriate homogeneous Dirichlet conditions where each of which admits an inverse operator commonly known as the Green operator GΩ. Under mild conditions on L and its Green operator, we establish various sharp compactness of GΩ involving weighted Lebesgue spaces and weighted measure spaces. These results are then employed to prove the solvability for semilinear elliptic equation Lu+g(u)=μ in Ω with boundary condition u=0 on ∂Ω or exterior condition u=0 in RN∖Ω if applicable, where μ is a Radon measure on Ω and g:R→R is a nondecreasing continuous function satisfying a subcriticality integral condition. When g(t)=|t|p-1t with p>1, we provide a sharp sufficient condition expressed in terms of suitable Bessel capacities for the existence of a solution. The contribution of the paper consists of (i) developing novel unified techniques which allow to treat various types of fractional operators and (ii) obtaining sharp compactness and existence results in weighted spaces, which refine and extend several related results in the literature.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA22-17403S" target="_blank" >GA22-17403S: Nonlinear Schrödinger equations and systems with singular potentials</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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